{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from numpy.linalg import det"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = \"retina\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use(\"seaborn\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Chapter 1: Introduction\n",
    "\n",
    "## Bayesian Probabilities\n",
    "Consider a probability distribution driven by a set of parameters $w$ and observed data $D$. Depending on the point of view about $w$  we might consider knowing the *true* value of $w$ considering $D$ in the following two ways:\n",
    "\n",
    "* **frequentist POV**: $w$ is unique but unknown, we can estimate how close we are to $w$ via $D$\n",
    "* **bayesian POV**: $D$ is unique (the one observed); $w$ is a random variable (might change, we will see its effect once in $D$)\n",
    "\n",
    "\tIn both the frequentist POV and the bayesian POV we make use of MLE $\\mathbb{P}(D|w)$ . In ML, the negative log-likelyhood is known as the **error function**\n",
    "\n",
    "$$\n",
    "\tp(w | D) = \\frac{p(D|w)p(w)}{p(D)}\n",
    "$$\n",
    "\n",
    "Where,\n",
    "* $p(w|D)$ is the uncertainty in $w$ after having observed $D$\n",
    "* $p(w)$ is the prior probability distribution; where we capture our prior  beliefs\n",
    "* $p(D|w)$ is the likelyhood function. It expresses how probable is the observed data for different values of $w$\n",
    "\n",
    "### The Gaussian Distribution\n",
    "The gaussian distribution is defined in the following way:\n",
    "$$\n",
    "    \\mathcal{N}(x | \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}e^{-\\frac{1}{2\\sigma^2}(x - \\mu)^2}\n",
    "$$\n",
    "\n",
    "An alternative way to represent a gaussian distribution is by considering a *precision* term denoted by $\\beta := 1 / \\sigma^2$\n",
    "$$\n",
    "    \\mathcal{N}(x | \\mu, \\beta^{-1}) = \\frac{\\beta^{1/2}}{\\sqrt{2\\pi\\sigma^2}}e^{-\\frac{\\beta}{2}(x - \\mu)^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fdc47070750>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 329,
       "width": 487
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def norm_pdf(x, mu, sigma2): return 1 / np.sqrt(2 * np.pi * sigma2) * np.exp(-(x - mu)**2 / (2 * sigma2))\n",
    "xrange = np.linspace(-4, 4, 100)\n",
    "plt.plot(xrange, norm_pdf(xrange, 0, 1), label=r\"$\\mu=0; \\ \\sigma^2=1$\")\n",
    "plt.plot(xrange, norm_pdf(xrange, 1, 2), label=r\"$\\mu=1; \\ \\sigma^2=2$\")\n",
    "plt.plot(xrange, norm_pdf(xrange, -1, 3), label=r\"$\\mu=-1; \\ \\sigma^2=3$\")\n",
    "plt.legend(fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The gaussian distribution defined over a $D$ dimensional vector $X$ is\n",
    "\n",
    "$$\n",
    "    \\mathcal{N}(X | \\mu, \\Sigma) = \\frac{1}{(2\\pi)^{D/2}\\det(\\Sigma)^{1/2}}\\exp\\left(-\\frac{1}{2}(x - \\mu)^T\\Sigma^{-1}(x - \\mu)\\right)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.linalg import inv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xrange = np.mgrid[-3:3:0.1, -3:3:0.1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "Sigma = np.array([[0.1, -0.8]]).T\n",
    "Sigma = np.exp(Sigma @ Sigma.T)\n",
    "\n",
    "def norm_pdf_v(X, mu, sigma):\n",
    "    diff_term = (X - mu[:, None])\n",
    "    D = len(X)\n",
    "    den = (2 * np.pi) ** (D / 2) * np.sqrt(det(sigma))\n",
    "    num = np.einsum(\"inm,ij,jnm->nm\", diff_term, inv(sigma), diff_term)\n",
    "    num = np.exp(-num / 2)\n",
    "    return num / den"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 346,
       "width": 479
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Multivariate Normal\", fontsize=15)\n",
    "plt.contourf(*Xrange, norm_pdf_v(Xrange, mu0, Sigma), cmap=\"viridis\", levels=20);"
   ]
  }
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